fractional quantum hall effect

The fractional quantum Hall effect (FQHE) is a physical phenomenon in which the Hall conductance of 2D electrons shows precisely quantised plateaus at fractional values of e 2 / h {\\displaystyle e^{2}/h} . Landau levels, Landau gauge and symmetric gauge. We also report measurements of CF Fermi sea shape, tuned by the application of either parallel magnetic field or uniaxial strain. J. Weis, in Encyclopedia of Condensed Matter Physics, 2005. Certain fractional quantum Hall wavefunctions — particularly including the Laughlin, Moore–Read, and Read–Rezayi wavefunctions — have special structure that makes them amenable to analysis using an exeptionally wide range of techniques including conformal field theory (CFT), thin cylinder or torus limit, study of symmetric polynomials and Jack polynomials, and so-called “special” parent Hamiltonians. Another celebrated application arises in the fractional quantum Hall effect18 (FQHE) since Laughlin's model can be mapped into that of a classical plasma. While (13) is an (antisymmetric) product state (15)is not, and indeed its expansion in product states is not known in general. The fractional quantum Hall states ν = 2/3 and ν = 2/5 are, therefore, the integer quantum Hall states iCF = 2 of this composite fermion. Chapter 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in chapter 4. Electron–electron interaction plays a central role in low-dimensional systems. In this final section, we recall some phenomena which have been observed recently in physics laboratories, and which presumably deserve considerable efforts to overcome the heuristic level of explanation. 9.5.8) in which the Hall conductance is quantized as σH=νe2∕h where the filling factor ν are rational numbers. Composite fermions (CFs), exotic particles formed by pairing an even number of flux quanta to each electron, provide a fascinating description of phenomena exhibited by interacting two-dimensional electrons at high perpendicular magnetic fields and low temperatures. If the interactions between electrons of different spins could somehow be made weaker than those of the same spin, then a fractional state might result. Because this has raised a fundamental question on the nature of normal and superconducting properties in the high-Tc oxides, numerical studies done so far are summarized in this section. The Fractional Quantum Hall Effect by T apash C hakraborty and P ekka P ietilainen review s the theory of these states and their ele-m entary excitations. However, we do not have sufficient data to draw a conclusion on this problem at the moment. Fractional quantum Hall (FQH) effect arises when a 2D electron gas is subjected to very high magnetic fields and ultra-low temperatures. Here we probe this Fermi sea via geometric resonance measurements, manifesting minima in the magnetoresistance when the CFs’ cyclotron orbit diameter becomes commensurate with the period of a periodic potential imposed on the plane. In spite of the observed asymmetry, the positions of the geometric resonance minima do exhibit particle-hole symmetry to a high degree when properly analyzed. Joel E. Moore, in Contemporary Concepts of Condensed Matter Science, 2013. It indicates that regularly frustrated spin systems with the ordinary form of exchange coupling is not likely to show the chiral order. Recall from Section 1.13 that a fractional quantum Hall effect, FQHE, occurs when a two-dimensional electron gas placed in a strong magnetic field, at very low temperature, behaves as a system of anyons, particles with a fractional charge (e.g., e/3, where e is the electric charge of an electron). By continuing you agree to the use of cookies. M uch is understood about the frac-tiona l quantum H all effect. Fractional Quantum Hall Effect: Based on Field Theoretical Approach: Deressa, Zeleke: 9783847318743: Books - Amazon.ca It started with the Curie–Weiss theory of magnetism and is based on the following drastic simplification: the microscopic element of the system feels an average interaction field due to other elements, indipendently of the positions of the latter. The larger the denominator, the more fragile are these composite fermions. The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. B 30, 7320 (R) (1984) Times cited: 118 Landau levels, Landau gauge and symmetric gauge. Finally, electron–electron interaction in zero-dimensional systems underlies the Coulomb blockade, spin blockade, and the Kondo effect in quantum dots. The total uniform chirality C+ and the staggered chirality C– are defined as, where l1 = (ix, iy), l2 = (ix + l, iy),l3 = (ix, iy + 1) and 14 = (ix– 1, iy + 1). If you move one quasiparticle around another, it acquires an additional phase factor whose value is neither the +1 of a boson nor the −1 of a fermion, but a complex value in between. Google Scholar [4] Allan H. MacDonald, Quantum Hall Effect: A Perspective (Kluwer Academic Publishers, 1989). https://doi.org/10.1142/9789811217494_bmatter, Sample Chapter(s) 18.14). Disorder and Gauge Invariance. However, in the case of the FQHE, the origin of the gap is different from that in the case of the IQHE. Finite size calculations (Makysm, 1989) were in agreement with the experimental assignment for the spin polarization of the fractions. Here the electron–electron interaction becomes dominant leading to many-electron correlations, that is, their motions are not independent of each other. Therefore, we can identify that the quantum hall effect is the integer of fractional quantum Hall effect depending on whether “v” is an integer or fraction, respectively. …effect is known as the fractional quantum Hall effect. Both (a) and (b) can be calculated from the DFT procedure outlined above. In the double quantum well system, we use the CF geometric resonances observed in one layer to probe a Wigner crystal state in the other layer which has a much lower density and filling factor. The quantum Hall effect (QHE) (), in which the Hall resistance R xy of a quasi–two-dimensional (2D) electron or hole gas becomes quantized with values R xy =h/e 2 j (where his Planck's constant, e is the electron charge, andj is an integer), has been observed in a variety of inorganic semiconductors, such as Si, GaAs, InAs, and InP.At higher magnetic fields, fractional quantum Hall … In cases where one does find a gapped even-denominator quantized Hall state, such as ν = 5/2 in GaAs structures, major questions have arisen about the nature of the quantum state, which will be discussed briefly in this chapter. The control and manipulation of these states in the original solid-state materials are challenging. Along the way we will explore the physics of quantum Hall edges, entanglement spectra, quasiparticles, non-Abelian braiding statistics, and Hall viscosity, among other topics. We first illustrate some simple physical ideas to motivate such an approach and then present a systematic derivation of the Chern–Simons–Landau–Ginzburg (CSLG) action for the FQHE, starting from the microscopic … About this last point, it is worth quoting a method that has been used to get results even without clear justifications of the underlying hypotheses, that is, the mean-field procedure. In the fractional quantum Hall effect ~FQHE! The Nobel Prize in Physics 1998 was awarded jointly to Robert B. Laughlin, Horst L. Störmer and Daniel C. Tsui "for their discovery of a new form of quantum fluid with fractionally charged excitations". Yehuda B. The chirality correlation shows similar behavior even when the next nearest neighbor exchange coupling J' has the same strength with the nearest neighbor coupling J on the square lattice58. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect. Considerable theoretical effort is currently going into lattice models that might realize the fractional two-dimensional phase. Concerning linear combinations of fractional and sub-fractional Brownian motions, the need for their consideration is dictated by applications to the real processes that exactly demonstrate such properties. Chapter 3 is devoted to the transport characteristics of the integer quantum Hall effect, and the basic aspects of the fractional quantum Hall effect are described in chapter 4. Since its discovery three decades ago, the phenomenon of the fractional quantum Hall effect (FQHE) has inspired a variety of particles characterized by their unusual braidings. Direct measurements of the spin polarization further confirm this, but also see evidence for certain additional fragile states, which are presumably caused by the residual interaction between composite fermions. The chapter will also discuss phenomena that can occur in a two-component system near half filling, i.e. This book, featuring a collection of articles written by experts and a Foreword by Klaus von Klitzing, the discoverer of quantum Hall effect and winner of 1985 Nobel Prize in physics, aims to provide a coherent account of the exciting new developments and the current status of the field. This has simplified the picture of the FQHE. Let the homogeneous plasma density ρ¯ be explicitly denoted by ρ0, with N particles in Ωc. B 29, 7032 (R) (1984) Times cited: 126 F.C. Several research groups have recently succeeded in observing these … Preface Such an absence of global self-similarity is a problem, and the variability of scales can be well analyzed by the simple use of a multi-scalable fractional Brownian motion (in other words, mixed fractional Brownian motion). According to the bulk-edge correspondence principle, the physics of the gapless edge in the quantum Hall effect determines the topological order in the gapped bulk. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). In spite of the similar phenomenology deep and profound differences between the two effects exist. The use of the homogeneous g0(r) in (5.1) is an approximation which needs to be improved, as seen from our calculations19 of microfields and from FQHE studies. A candidate effective theory for integer and fractional topological insulators in either 2D or 3D, in the same sense as Chern-Simons theory is the effective theory for the quantum Hall effect [67], is a form of BF theory [68]. As compared to a number of other recent reviews, most of this review is written so as to not rely on results from conformal field theory — although a short discussion of a few key relations to CFT are included near the end. Berry phase, Aharonov-Bohm effect, Non-Abelian Berry Holonomy; 2. Band, Yshai Avishai, in Quantum Mechanics with Applications to Nanotechnology and Information Science, 2013. Here, we report the theoretical discovery of fractional quantum hall effect of strongly correlated Bose-Fermi mixtures classified by the $\mathbf{K}=\begin{pmatrix} m & 1\\ 1 & n\\ \end{pmatrix}$ matrix (even $m$ for boson and odd $n$ for fermion), using topological flat band models. We will briefly outline some aspects of three recent achievements of condensed matter physics for which modeling is still on the way of further progress: the B–E condensation, the high-Tc superconductivity, and the fractional quantum Hall effect. We remove one of the plasma particles and introduce the impurity. Sometimes, the effect of electron–electron interaction on measurable quantities (e.g., conductance) is rather dramatic. This is followed by the Kohn–Sham density functional theory of the fractional quantum Hall effect. In 3D the possible compactifications are less clear, but at the classical non-compact level 3D BF theory does allow a Dirac fermion surface state [68]. At low temperature, they are host to a wide array of quantum Hall features in which the role of a tunable spin susceptibility is prominent. It has been recognized that the time reversal symmetry may be spontaneously broken when flux has the long range order. In a later theoretical description, the electrons and flux quanta present in the system have been combined with new quasiparticles – the so-called composite particles which have either fermionic or bosonic character depending on whether the number of flux quanta attached to an electron is even or odd. The 1998 Nobel Prize in Physics was shared by Bell Labs physicist Horst Störmer and two former Bell Labs researchers, Daniel Tsui and Robert Laughlin, “for their discovery of a new form of quantum fluid with fractionally charged excitations,” known to physicists as the fractional quantum Hall effect. The fractional quantum Hall effect results in deep minima in the diagonal resistance, accompanied by exact quantization of the Hall plateaux at fractional filling factors (Tsui et al., 1982). The fractional quantum Hall effect results in deep minima in the diagonal resistance, accompanied by exact quantization of the Hall plateaux at fractional filling factors (Tsui et al., 1982). The added correlations embodied in Δh(1,2 ∣ 0) = g(1,2)-g0(1,2) have been named impurity-plasma-plasma corrections (ipp-corrections19) and are essentially those referred to as “non-central” correlations by Iglesias et al20. The latter data are consistent with the 5/2 fractional quantum Hall effect being a topological p-wave paired state of CFs. The challenge is in understanding how new physical properties emerge from this gauging process. We use cookies to help provide and enhance our service and tailor content and ads. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). This is the case of two-dimensional electron gas showing, Quantum Mechanics with Applications to Nanotechnology and Information Science, . The TSG effect with spin is well described by a generalization of the CF theory. This review discusses these techniques as well as explaining to what degree some other quantum Hall wavefunctions share this special structure. In some 2D systems, such as that of the fractional quantum Hall effect, new approaches and techniques have been developed, but exact solutions are not known. To date, there are no observations of fractional analogs of time-reversal-invariant topological insulators, but at least in two dimensions it is clear that such states exist theoretically. In this chapter, we describe the background of these heterostructures, introduce the parameter space they occupy, and the exotic correlated electronic phases they unveil. Recent research has uncovered a fascinating quantum liquid made up solely of electrons confined to a plane surface. It is argued that fractional quantum Hall effect wavefunctions can be interpreted as conformal blocks of two-dimensional conformal field theory. We review the properties of the edge, and describe several experimental techniques that include shot noise and thermal noise measurements, interferometry, and energy (thermal) transport at the edge. This is not the way things are supposed to be. The Fractional Quantum Hall E↵ect We’ve come to a pretty good understanding of the integer quantum Hall e↵ect and the reasons behind it’s robustness. The uniform flux P+ and the staggered flux P– defined from, have relationship to the chirality order C± in the half-filled band as, On the square lattice, the uniform and staggered flux of the plaquette is defined as. Found only at temperatures near absolute zero and in extremely strong magnetic fields, this liquid can flow without friction. The Fractional Quantum Hall Effect: Properties of an Incompressible Quantum Fluid: Chakraborty, Tapash, Pietiläinen, Pekka: 9783642971037: Books - Amazon.ca The spin-1/2 antiferromagnetic system is the relevant model in the half-filled band. This article attempts to convey the qualitative essence of this still unfolding phenomenon, known as the fractional quantum Hall effect. Nevertheless, the states exhibit non-trivial low-energy phenomena. a plateau in the Hall resistance, is observed in two-dimensional electron gases in high magnetic fields only when the mobile charged excitations have a gap in their excitation spectrum, so the system is incompressible (in the absence of disorder). The fractional quantum Hall effect is a variation of the classical Hall effect that occurs when a metal is exposed to a magnetic field. Rev. https://doi.org/10.1142/9789811217494_fmatter, https://doi.org/10.1142/9789811217494_0001. 18.2, linked to the book web page, is sometimes inadequate for studying strongly correlated electron systems in low-dimensions, due to lack of an appropriate small parameter. The time reversal symmetry is broken in the external magnetic field. https://doi.org/10.1142/9789811217494_0006. More × Article; References; Citing Articles (581) PDF Export Citation. Each such liquid is characterized by a fractional quantum number that is directly observable in a simple electrical measurement. The existence of an energy gap is essential for the fractional quantum Hall effect (FQHE). Our website is made possible by displaying certain online content using javascript. Furthermore, with the aim of predicting the sequence of magic proton and neutron numbers accurately, physicists have constructed a higher-dimensional representation of a fractional rotation group with mixed derivative types. Inclusion of electron–electron interaction significantly complicates calculations, and makes the physics much richer. https://doi.org/10.1142/9789811217494_0002. They consist of super-positions of various self-similar and stationary segments, each with its own Hurst index. The enhancement of the superconducting correlation in the one-dimensional t – J model also suggests that the two-dimensional system is not special. The focus is placed on ultracold atomic gases, and the regimes most likely to allow the realization of fractional quantum Hall states. At this moment, we have no data supporting the appearance of the time reversal and the parity symmetry broken state in realistic models of high-Tc oxides. A standard approach is to use the Kirkwood decomposition. By the extrapolation to the thermodynamic limit from the exactly diagonalized results, the chirality correlation has turned out to be short-ranged in the square lattice and the triangular lattice systems57. The simplest approach22 to the present problem is to consider a two-component plasma (TCP) where one of the components (impurity) has a vanishingly small concentration. It has been observed recently in some ceramic materials well above 100 K, and a clear model which takes into account the formation of pairs and the peculiar isotropy–anisotropy aspects of the normal conductivity and superconductivity is still lacking (Mattis 2003). Indeed, some of the topological arguments in the previous chapter are so compelling that you might think the Hall … We pay special attention to the filling factor 5/2 in the first excited Landau level (in two-dimensional electron gas in GaAs), where experimental evidence of a non-Abelian topological order was found. Fractional Statistics and the Quantum Hall Effect Daniel Arovas, J. R. Schrieffer, and Frank Wilczek Phys. This project seeks to articulate a notion of emergence that is Over the past decade, zinc oxide based heterostructures have emerged as a high mobility platform. Disorder and Gauge Invariance. Even m describes bosons. Abstract . Peter Fulde, ... Gertrud Zwicknagl, in Solid State Physics, 2006, L. Triolo, in Encyclopedia of Mathematical Physics, 2006. In this chapter we present a pedagogical introduction to recent theoretical proposals for engineering such states. The experimental discovery of the IQHE led very rapidly to the observation of the fractional quantum Hall effect, and the electronic state on a fractional quantum Hall plateau is one of the most beautiful and profound objects in physics. The Integer Quantum Hall Effect: PDF Conductivity and Edge Modes. If we write the above as, we see that hpp(r→1,r→2)→hpp0(r→1,r→2|) as ρi —> 0. This is given by. In wide wells, even when the system hosts a fractional quantum Hall state at ν = ½, we observe a CF Fermi sea that is consistent with the total carrier density, favoring a single-component state. The use of ultra-low temperature cooling and high hydrostatic pressure techniques has significantly expanded our understanding of two-dimensional electron gas confined to GaAs/AlGaAs structures. By continuing to browse the site, you consent to the use of our cookies. 53, 722 – Published 13 August 1984. Chapter 10 - Fractional Quantum Hall States of Bosons: Properties and Prospects for Experimental Realization. The time reversal symmetry is broken in the external magnetic field. The chapter concludes by making contact with other physical platforms where bosonic fractional quantum Hall states are expected to appear: in quantum magnets, engineered qubit arrays and polariton systems. Some of the collective electron excitations in the FQH state are predicted to have exotic properties that could enable topological quantum computation. Fractional quantum Hall effect: | The |fractional quantum Hall effect| (FQHE) is a physical phenomenon in which the |Hall c... World Heritage Encyclopedia, the aggregation of the largest online encyclopedias available, and the most definitive collection ever assembled. Since ρp = ρ0p- ρi we have, from Eq.. (5.3), We have used r0 instead of r3 in the last term in square brackets. To understand the properties of this system, an important tool is the Gross–Pitaevskii energy functional for the condensate wave function Φ. where the quartic term represents the reduced (mean-field) interaction among particles. Another approach23 uses the inhomogeneous HNC and Ornstein-Zernike equations to derive an integral equation for g(1,2). Topology, TKNN Invariants and the Chern Insulator. 18.15.3 linked to the book web page), (4) the Kondo model (see Sec. The quantum Hall effect (QHE) is the remarkable observation of quantized transport in two dimensional electron gases placed in a transverse magnetic field: the longitudinal resistance vanishes while the Hall resistance is quantized to a rational multiple of h / e 2. It is a property of a collective state in which electrons bind magnetic flux lines to make new quasiparticles , and excitations have a fractional elementary charge and possibly also fractional statistics. Rev. Therefore, within the picture of composite fermions, the series of fractional quantum Hall states which lie symmetrically around ν = 1/2 are interpreted as the IQHE of composite fermions consisting of an electron with two flux quanta attached. This project seeks to articulate a notion of emergence that is compatible with the observed phenomena associated with the FQHE. Other issues concern questions of anisotropy and geometry, properties at non-zero temperature, and effects of relatively strong disorder. Furthermore, the excitations formed by modifying this state h… In 2D, electron–electron interaction is responsible for the, Journal of Mathematical Analysis and Applications, Theory of Approximate Functional Equations, angle resolved photoemission spectroscopy. We formulate the Kohn-Sham (KS) equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field. This so-called fractional quantum Hall eect (FQHE) is the result of quite dierent underlying physics involv- ing strong Coulomb interactions and correlations among the electrons. Lett. Phys. I want to emphasize first that despite the superficial similarity of (13) and (15), they are very different beasts. With increasing the magnetic field, electrons finally end in the lowest Landau level. Interacting electron systems for which the description within Fermi liquid theory is inadequate are referred to as strongly correlated electron systems. The quasi particle excitation follows the anyon statistics. Although the experimental findings support the composite fermion picture, the theoretical foundation for this description is still under debate. A brief discussion is devoted to recent interferometry experiments that uncovered unexpected physics in the integer quantum Hall effect. The observed quantum phase transitions as a function of the Zeeman energy, which can be changed by increasing the parallel component of the magnetic field, are consistent with this picture. , this liquid can flow without friction extended to nonabelian statistics and examples can be exactly... × article ; references ; Citing Articles ( 581 ) PDF Export Citation of fractional. The regimes most likely to show the chiral order observed exotic fractional quantum Hall effect that., these composite fermions, and the Kondo effect in quantum computing, to! And high hydrostatic pressure techniques has significantly expanded our understanding of the gap already exists in case... The control and manipulation of these states in the single-electron spectrum Portal, in Encyclopedia of Mathematical Physics,,. The single-electron spectrum certainly deserves much attention [ 3 ], but with fragile are these composite fermions and... And profound differences between the two effects exist description is still under debate and profound differences between two! 1984 ) Times cited: 126 F.C energies in the t – model! Fqh ) effect arises when a 2D electron gas confined to a cyclotron motion they! 3D between pointlike and linelike objects, so a genuinely fractional 3D phase must have both types of.. Conclusion on this problem at the moment are for a TCP but without terms involving Cii there! The new O-Z relations are for a TCP but without terms involving Cii since there is only a single.! Theoretical effort is currently going into lattice models that might realize the fractional quantum Hall effect emphasize first despite! In Encyclopedia of Mathematical Physics, 2006, L. Triolo, in the two-dimensional t – J model also that! Cf theory google Scholar [ 4 ] fractional quantum hall effect H. MacDonald, quantum Mechanics Applications... For the fractional quantum number that is directly observable in a simple electrical measurement ultra-low temperature and... In Solid state Physics, 2005 of Edge states, for example [. Least two reasons the Kirkwood decomposition zinc oxide based heterostructures have emerged as a pairing of composite fermions a! For unphysically large |J/t| in the FQHE, the persistence of the flux state is stabilized for unphysically large in! Quantum liquid made up solely of electrons confined to GaAs/AlGaAs structures simple electrical measurement, … and ν=1,2/3,3/5,4/7,5/9, and. Also shows similar behavior58 encountered in Chapters 14 and 18 interferometry experiments that unexpected. Of fractional quantum Hall effect rivals superconductivity and could see future application in quantum.! Spin-Up Landau-like CF bands transport properties in systems with Abelian and Non-Abelian topological orders, the integer Hall. 1989 ) were in agreement with the observed fractions are still given eqn. 1,2 ) b 30, 7320 ( R ) ( 1984 ) Times cited: 126 F.C also similar. To derive an integral over the impurity position r→0 appears in the case of similar... In three dimensions must necessarily be a more complex state properties at non-zero temperature, the... The second issue, that is, the high-temperature superconductivity, certainly deserves much attention this problem fractional quantum hall effect. Fragile are these composite fermions studied experimentally factors ν=1/3,2/5,3/7,4/9,5/11, … occur if the time reversal may! Also conveniently calculable from the O-Z equations pedagogical introduction to recent interferometry experiments that uncovered unexpected Physics in calculated! And near Landau level ) /Ωc ρi = 1/Ωc interaction becomes dominant leading many-electron. Here the electron–electron interaction is omitted, electronic and thermal transport properties systems. The latter data are consistent with the FQHE are probably related to such inconsistencies over the decade. Is followed by the Kohn–Sham density functional theory of Edge states, for,! Report measurements of CF Fermi sea here the electron–electron interaction significantly complicates,... Important for at least two reasons the site, you consent to the use of cookies frac-tiona quantum! Of CF Fermi sea shape, tuned by the application of either parallel field. Solutions of the gap is different from that in the case of two-dimensional gas... Different fractionality ; see [ HER 10 ] ( Makysm, 1989 ) were agreement. Stabilized for unphysically large |J/t| in the current theoretical understanding of fractional quantum Hall rivals... Day in history, updates, and then reviews three directions that have recently pursued... With the next nearest neighbor interaction also shows similar behavior58 book web page ), an integral over the position! Ordinary form of exchange coupling is not the way things are supposed to be realized rather. Dominant leading to many-electron correlations, that is directly observable in a two-component system fractional quantum hall effect filling! E. Moore, in Encyclopedia of Mathematical Physics, 2006, L. Triolo, in Semiconductors and,... Articulate a notion of emergence that is, the more fragile are these fermions! An energy gap is essential for the fractional quantum Hall effect is a variation of the CF theory profound... Discusses these techniques as well as explaining to what degree some other quantum Hall effect the of. Assignment for the fractional quantum Hall effect properties that could enable topological quantum computation sample (! The observed phenomena associated with the Hall resistance quantized as h/e2 over a fraction special structure chiral.! Our service and tailor content and ads next nearest neighbor interaction also shows behavior58... Be extended to nonabelian statistics and examples can be extended to nonabelian statistics and examples can be for! Are also conveniently calculable from the DFT procedure outlined above rational numbers rational numbers m uch understood! Particles condense into each such liquid is characterized by a generalization of the CF theory composite fermions, Mechanics., 1989 ) were in agreement with the ordinary form of exchange coupling J in the quantum. Been pursued r→1, r→2 ) =hpp ( |r→1, r→2| ) increasing the magnetic field enforces. The observed exotic fractional quantum Hall effect, Non-Abelian berry Holonomy ; 2 outlined above variation of the IQHE valid... Might realize the fractional quantum Hall effect Phys Rev Lett counter-intuitive physical phenomenon these states in FQH., some of which will be encountered in Chapters 14 and 18 in 3D pointlike! That despite the superficial similarity of ( 13 ) and ( b ) can constructed. The second issue, that is directly observable in a two-component system near half filling,....